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Arimotech is doing some consulting for helping and expanding use of simulation techniques on distortion and residual stress in parts, which are induced through a chain of manufacturing processes.


Introduction to distortion and residual stress


Unavoidable distortion in parts is produced after manufacturing processes. On the following linked page, quench distortions of a shaft with a keyway parallel to its length are shown as two movies, although these are not in commercial products.


Quench distortion (on the page in Prof. H. K. D. H. Bhadeshia's Website)


The origin of this distortion was explained by Dr. Arimoto et al. as shown in the following paper.


K. Arimoto et al., Explanation of the Origin of Distortion and Residual Stress in Specimens Using Computer Simulation, Proc. 5th International Conference and European Conference on Heat Treatment 2007, Berlin, 25-27, April., 2006, pp. 157-164.


The origin of distortion can be explained by examining simulated results, especially for distributions of strains along a specific line in a body. Simulation shows us so many kinds of quantities, which are related each other. For example, strains such as total, elastic, thermal, plastic, transformation, transformation and plastic strains are controlled by the equilibrium equation as shown schematically in the following figure at the arbitrary time t.


Some strains are determined by the influences from an environment. For example, thermal strain is related to temperature changes, and transformation strain is produced by microstructural changes in phase transformations. On the other hand, elastic strain corresponds to the current stress directly based on their inherent characteristics. Also deviatoric components of stress are effective to plastic and transformation plastic strains. It is noted that transformation plastic strain needs not only stress but also phase transformations. Finally summation of total strain in a body corresponds to its distortion.


It is clear distortion and stress at the final stage is resulted from so many phenomena relating to the changes of each strain during processes. An inherent shape of the body and its constraints are also affected to the distortion and residual stress.


Development of simulation tool


Arimotech is developing a simulation tool, MUSIMAP, for their R & D and consulting purpose. MUSIMAP is the Multiphysical Simulation Tool for Manufacturing Chains and Life Cycles of Parts, Its details are shown on the following linked pages.

     Link to the English page of the MUSIMAP information


Educational programs


Understanding the origin of phenomena is very effective to solve particular problems under any circumstances. However the knowledge over mechanical and material engineering fields is necessary to explaining the origin of distortion and residual stress. Difficulties of the interdisciplinary research may be one of the reasons why this explanation has been delayed for a long period of time.


Arimotech provides an educational program for understanding the origin depending on customers. The following texts have been written for this purpose.

"Heat Treating Distortion and Residual Stresses-Explanation of their Generation Mechanism Using Computer Simulation", Part 1&2, in Japanese.  

The contents of text in English: linked PDF file.


Prat 1 in Japanese: linked PDF file. 

Prat 2 in Japanese: linked PDF file. 


Chapter 5 "Heat conduction and heat transfer" of the text in English: linked PDF file 

"Review of Researches for Evaluating Nitriding Simulation Models", 145 pages, in Japanese.

The contents and references in English : linked PDF file.


Research and development


It is necessary to improve numerical models for enhancing an accuracy of the simulation on distortion and residual stresses. Dr. Arimoto has been involved in this kind of activities, and presented his results at several international conferences. He was a member of the international committee of "3rd International Conference on Distortion Engineering" in 2011 in Bremen, Germany.


"Distortion Engineering" is subject of the Collaborative Research Center established at the University of Bremen in 2001. The center is named as SFB570.